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Title: Analytic transfer in K-homology for stratified spaces
Abstract: The classical umkehr map of Hopf assigns to a map of oriented manifolds, f:M -> N, `wrong-way' homomorphisms in homology, f_!: H_*(N) -> H_*(M), and in cohomology, f^!:H^*(M) -> H^*(N), the latter a version of `integration over the fibers'. Similar wrong-way maps, sometimes known as transfer maps or Gysin maps, are defined for other generalized (co)homology theories as long as the manifolds are suitably oriented and have had many applications. While these maps are defined only for manifolds there has long been interest in extending them to singular spaces. I'll discuss joint work with Markus Banagl and Paolo Piazza in which we capitalize on recent work on the index theory of signature operators to give analytic definitions of transfer maps in K-homology for stratified spaces and relate them to topological orientations.